We examine theoretically a possibility of ferroelectricity caused by electronic charge order without inversion symmetry, motivated by layered iron oxides. Quantum electronic models in a paired-triangular lattice are analyzed by utilizing the variational Monte Carlo simulation. Our calculation demonstrates that combined effects of electron transfer between the layers, corresponding to quantum fluctuation between the potential minima, and geometrical frustration promote appearance of an electric polarization. Present results are in contrast to the conventional manner of quantum fluctuation in ferroelectricity.
The temperature dependence of charge order in Fe2OBO3 was investigated by resistivity and differential scanning calorimetry measurements, Mossbauer spectroscopy, and synchrotron x-ray scattering, revealing an intermediate phase between room temperature and 340 K, characterized by coexisting mobile and immobile carriers, and by incommensurate superstructure modulations with temperature-dependent propagation vector (1/2,0,tau). The incommensurate modulations arise from specific anti-phase boundaries with low energy cost due to geometrical charge frustration.
We study phase diagrams of the Hubbard model on anisotropic triangular lattices, which also represents a model for $κ$-type BEDT-TTF compounds. In contrast with mean-field predictions, path-integral renormalization group calculations show a universal presence of nonmagnetic insulator sandwitched by antiferromagnetic insulator and paramagnetic metals. The nonmagnetic phase does not show a simple translational symmetry breakings such as flux phases, implying a genuine Mott insulator. We discuss possible relevance on the nonmagnetic insulating phase found in $κ$-(ET)$_2$Cu$_2(CN)_3$.
We systematically derive low-energy effective Hamiltonians for molecular solids $β^\prime$-$X$[Pd(dmit)$_{2}$]$_{2}$ ($X$ represents a cation) using ab initio density functional theory calculations and clarify how the cation controls the inter-dimer transfer integrals and the interaction parameters. The effective models are solved using the exact diagonalization method and the antiferromagnetic ordered moment is shown to be significantly suppressed around the spin-liquid candidate of $X$=EtMe$_{3}$Sb, which is reported in experiments. We also show that both the geometrical frustration and the …
The Hubbard model with geometrical frustration is investigated in a metallic phase close to half-filling. We calculate the single particle spectral function for the triangular lattice within dynamical cluster approximation, which is further combined with non-crossing approximation and fluctuation exchange approximation to treat the resulting cluster Anderson model. It is shown that frustration due to non-local correlations suppresses short-range antiferromagnetic fluctuations and thereby assists the formation of heavy quasi-particles near half-filling.
We report on the emergence of antiferromagnetic spin chains from two-dimensionally aligned spins on the anisotropic triangular lattice (ATL) in the insulating calcium rhenium oxychloride Ca3ReO5Cl2. The compound contains Re6+ ions each with one unpaired electron in the dxy orbital, which are arranged to form a spin-1/2 ATL with J'/J ~ 0.32 and J = 41 K, where J and J' are magnetic interactions in and between the chains, respectively. In spite of the apparent two dimensionality, we observe clear evidence of a gapless spin liquid that is characteristic of the spin-1/2 Heisenberg chain. This one-…
CaBaCo4O7 represents a new class of ferrimagnets whose structure is built up of CoO4 tetrahedra only, similarly to other members LnBaCo4O7 of the 114 series, forming an alternate stacking of kagome and triangular layers. Neutron powder diffraction reveals, that this compound exhibits the largest distortion within the 114 series, characterized by a strong buckling of the kagome layers. Differently from all other members it shows charge ordering, with Co2+ sitting on two sites (Co2, Co3) and mixed valent cobalt Co3+/Co2+L sitting on two other sites (Co1, Co4). The unique ferrimagnetic structure …
The small-cluster exact-diagonalization calculations and the projector quantum Monte Carlo method are used to examine the competing effects of geometrical frustration and interaction on ferromagnetism in the Hubbard model on the Shastry-Sutherland lattice. It is shown that the geometrical frustration stabilizes the ferromagnetic state at high electron concentrations ($n \gtrsim 7/4$), where strong correlations between ferromagnetism and the shape of the noninteracting density of states are observed. In particular, it is found that ferromagnetism is stabilized only for these values of frustrati…
To search for novel spin-charge coupled phenomena in the strongly correlated electron system on a frustration lattice, charge transport and dynamics have been investigated for the hole-doped spin-glass (Mott) insulator (Y$_{1-x}$Cd$_{x}$)$_{2}$Mo$_{2}$O$_{7}$ with pyrochlore structure. Coincident with the disappearance of spin-glass state by hole doping, a diffusive metallic transport with strongly renormalized electron mass shows up with no long range spin order, which is caused by strong antiferromagnetic spin fluctuation due to the geometrical frustration.
Geometrical frustration describes situations where interactions are incompatible with the lattice geometry and stabilizes exotic phases such as spin liquids. Whether geometrical frustration of magnetic interactions in metals can induce unconventional quantum critical points is an active area of research. We focus on the hexagonal heavy fermion metal CeRhSn where the Kondo ions are located on distorted kagome planes stacked along the c axis. Low-temperature specific heat, thermal expansion and magnetic Grüneisen parameter measurements prove a zero-field quantum critical point. The linear therma…
Hexagonal CeRhSn with paramagnetic $4f$ moments on a distorted Kagome lattice displays zero-field quantum critical behavior related to geometrical frustration. We report high-resolution thermal expansion and magnetostriction measurements under multiextreme conditions such as uniaxial stress up to 200 MPa, temperatures down to 0.1 K and magnetic fields up to 10 T. Under uniaxial stress along the $a$-direction, quantum criticality disappears and a complex magnetic phase diagram arises with a sequence of phases below 1.2 K and fields between 0 and 3 T ($\parallel a$). Since the Kondo coupling inc…
Physical properties of DyB$_4$ have been studied by magnetization, specific heat, and ultrasonic measurements. The magnetic entropy change and the ultrasonic properties in the intermediate phase II indicate that the degeneracy of internal degrees of freedom is not fully lifted in spite of the formation of magnetic order. The ultrasonic attenuation and the huge softening of $C_{44}$ in phase II suggests existence of electric-quadrupolar (orbital) fluctuations of the 4$f$-electron. These unusual properties originate from the geometrical quadrupolar frustration.
We calculated the phase diagram of the Kondo-Heisenberg model on two-dimensional honeycomb lattice with both nearest-neighbor and next-nearest-neighbor antiferromagnetic spin exchanges, to investigate the interplay between RKKY and Kondo interactions at presence of magnetic frustration. Within a mean-field decoupling technology in slave-fermion representation, we derived the zero-temperature phase diagram as a function of Kondo coupling $J_k$ and frustration strength $Q$. The geometrical frustration can destroy the magnetic order, driving the original antiferromagnetic (AF) phase to non-magnet…
We report on the muon spin rotation/relaxation study of a pyrochlore oxide, Cd2Os2O7, which exhibits a metal-insulator (MI) transition at T_{MI}~225 K without structural phase transition. It reveals strong spin fluctuation (>10^8/s) below the MI transition, suggesting a predominant role of geometrical spin frustration amongst Os^{5+} ions. Meanwhile, upon further cooling, a static spin density wave discontinuously develops below T_{SDW}~150 K. These observations strongly suggest the occurrence of an anomalous magnetic transition and associated change in the local spin dynamics in undistorted p…
We study the low-energy properties of the geometrically frustrated Hubbard model on a three-dimensional pyrochlore lattice and a two-dimensional checkerboard lattice on the basis of the renormalization group method and mean field analysis. It is found that in the half-filling case, a (semi-)metal to insulator transition (MIT) occurs. Also, in the insulating phase, which has a spin gap, the spin rotational symmetry is not broken, while charge ordering exists. The results are applied to the description of the MIT observed in the pyrochlore system ${\rm Tl_2Ru_2O_7}$.
We have characterized the magnetic and structural properties of the CdLn2Se4 (Ln = Dy, Ho), and CdLn2S4 (Ln = Ho, Er, Tm, Yb) spinels. We observe all compounds to be normal spinels, possessing a geometrically frustrated sublattice of lanthanide atoms with no observable structural disorder. Fits to the high temperature magnetic susceptibilities indicate these materials to have effective antiferromagnetic interactions, with Curie-Weiss temperatures theta ~ -10 K, except CdYb2S4 for which theta ~ -40 K. The absence of magnetic long range order or glassiness above T = 1.8 K strongly suggests that …
A structural and thermodynamic study of the newly synthesized single crystal Sr5Rh4O12 is reported. Sr5Rh4O12 consists of a triangular lattice of spin chains running along the c-axis. It is antiferromagnetically ordered below 23 K with the intrachain and interchain coupling being ferromagnetic (FM) and antiferromagnetic (AFM), respectively. There is strong evidence for an Ising character in the interaction and geometrical frustration that causes incomplete long-range AFM order. The isothermal magnetization exhibits two step-like transitions leading to a ferrimagnetic state at 2.4 T and a FM st…
We study the geometrical frustration of extended Hubbard model on diamond chain, where vertical lines correspond to the hopping and repulsive Coulomb interaction terms between sites, while the rest of them represent only the Coulomb repulsion one. The phase diagrams at zero temperature show quite curious phases: five types of frustrated states and four types of non-frustrated ones, ordered antiferromagnetically. Although decoration transformation was derived to spin coupling systems, this approach can be applied to electron coupling ones. Thus the extended Hubbard model can be mapped onto anot…
The interplay of Coulomb repulsion and geometrical frustration on charge-driven quantum phase transitions is explored. The ground state phase diagram of an extended Hubbard model on an anisotropic triangular lattice relevant to quarter-filled layered organic materials contains homogeneous metal, 'pinball' and three-fold charge ordered metallic phases. The stability of the 'pinball' phase occurring for strong Coulomb repulsions is found to be strongly influenced by geometrical frustration. A comparison with a spinless model reproduces the transition from the homogeneous metallic phase to a pinb…
In the eta-carbide-type correlated-electron metal Fe3Mo3N, ferromagnetism is abruptly induced from a nonmagnetic non-Fermi-liquid ground state either when a magnetic field (~14 T) applied to it or when it is doped with a slight amount of impurity (~5% Co). We observed a peak in the paramagnetic neutron scattering intensity at finite wave vectors, revealing the presence of the antiferromagnetic (AF) correlation hidden in the magnetic measurements. It causes a new type of geometrical frustration in the stellla quadrangula lattice of the Fe sublattice. We propose that the frustrated AF correlatio…
The ground-state properties of the two-dimensional Hubbard model with nearest-neighbor and next-nearest-neighbor hoppings at half filling are studied by the path-integral-renormalization-group method. The nonmagnetic-insulator phase sandwiched by the the paramagnetic-metal phase and the antiferromagnetic-insulator phase shows evidence against translational symmetry breaking of the dimerized state, plaquette singlet state, staggered flux state, and charge ordered state. These results support that the genuine Mott insulator which cannot be adiabatically continued to the band insulator is realize…
The geometrically-frustrated, triangular antiferromagnet GGG exhibits a rich mix of short-range order and isolated quantum states. We investigate the effects of up to 1% Neodymium substitution for Gallium on the ac magnetic response at temperatures below 1 K in both the linear and nonlinear regimes. Substitutional disorder actually drives the system towards a more perfectly frustrated state, apparently compensating for the effect of imperfect Gadolinium/Gallium stoichiometry, while at the same time more closely demarcating the boundaries of isolated, coherent clusters composed of hundreds of s…
We investigate the ground state of the Kondo necklace model on geometrically-frustrated lattices by the variational Monte Carlo simulation. To explore the possibility of a partially-ordered phase, we employ an extension of the Yosida-type wave function as a variational state, which can describe a coexistence of spin-singlet formation due to the Kondo coupling and magnetic ordering by the Ruderman-Kittel-Kasuya-Yosida interaction. We show the benchmark of the numerical simulation to demonstrate the high precision brought by the optimization of a large number of variational parameters. We discus…
Dimensionality is a critical factor in determining the properties of solids and is an apparent built-in character of the crystal structure. However, it can be an emergent and tunable property in geometrically frustrated spin systems. Here, we study the spin dynamics of the tetrahedral cluster antiferromagnet, pharmacosiderite, via muon spin resonance and neutron scattering. We find that the spin correlation exhibits a two-dimensional characteristic despite the isotropic connectivity of tetrahedral clusters made of spin 5/2 Fe3+ ions in the three-dimensional cubic crystal, which we ascribe to t…
Structural phase transition accompanying with quadrupolar ordering in DyB4 with Shastry-Sutherland type geometrical frustration has been studied by X-ray diffraction. Previous study [D. Okuyama et al.: J. Phys. Soc. Jpn. 74 (2005) 2434.] using resonant X-ray scattering revealed short-range ordering of the Ozx-type quadrupolar moments and the c-plane component of the magnetic moments in addition to long-range ordering of the c-axis component of the magnetic moments. The present report focuses on the lattice distortion below the quadrupolar ordering temperature at TN2=12.7 K. The (0 0 l=integer)…
We investigate the properties of an effective Hamiltonian with competing interactions involving spin and chirality variables, relevant for the description of the {\it trimerized} version of the spin-1/2 {\it kagome} antiferromagnet. Using classical Monte Carlo simulations, we show that remarkable behaviors develop at very low temperatures. Through an {\it order by disorder} mechanism, the low-energy states are characterized by a dynamical freezing of the chiralities, which decouples the lattice into ``dimers'' and ``triangles'' of antiferromagnetically coupled spins. Under the presence of an e…
In the present study we investigate the effects of geometrical frustration on the XY model with antiferromagnetic (AFM) coupling on a triangular lattice, generalized by the inclusion of a third-order antinematic term (AN3). We demonstrate that at non-zero temperatures such a generalization leads to a phase diagram consisting of three different quasi-long-range ordered (QLRO) phases. Compared to the model with the second-order AN coupling (AN2), it includes besides the AFM and AN3 phases which appear in the limits of relatively strong AFM and AN3 interactions, respectively, an additional comple…
The geometrically frustrated antiferromagnetic Swedenborgite DyBaCo$_{4}$O$_{7}$ is investigated by a combination of xray diffraction, magnetization and dielectric measurements. Systematic doping in the series Dy$_{1-x}$Ca$_{x}$BaCo$_{4}$O$_{7}$ causes a lifting of the geometrical frustration resulting in a structural transition from a Trigonal P31c to an orthorhombic Pbn2$_{1 }$ symmetry at $x=0.4$. This structural transition can also be accessed as a function of temperature, and all our orthorhombic specimens exhibit this transition at elevated temperatures. In line with previous reports, th…
We show that the electronic structures of the title compounds predicted by density functional theory (DFT) are well described by tight binding models. We determine the frustration ratio, J'/J, of the Heisenberg model on the anisotropic triangular lattice, which describes the spin degrees of freedom in the Mott insulating phase for a range of Pd(dmit)2 salts. All of the antiferromagnetic materials studied have J'/J < 0.5 or J'/J > 0.9, consistent with predictions for the Heisenberg model. All salts with 0.5 < J'/J < 0.9, where many-body theories find a number of competing ground states, are kno…
Competition between Geometrical Frustration and the Kondo Effect in CePdAl Revealed by High-Resolution Magnetization
Institute for Solid State Physics, The University of Tokyo（东京大学固体物理研究所）；Nagoya Institute of Technology（名古屋工业大学）；Institute for Materials Research, Tohoku University（东北大学物质材料研究所）；School of Science and Engineering, Chuo University（中央理工学院）；Department of Basic Science, The University of Tokyo（东京大学基础科学系）；Graduate School of Science and Engineering, Univ. of Toyama（富山理工学研究院）
The crystal structure and the magnetism of BaMn$_2$O$_3$ have been studied by thermodynamic and by diffraction techniques using large single crystals and powders. BaMn$_2$O$_3$ is a realization of a $S = 5/2$ spin ladder as the magnetic interaction is dominant along 180$^\circ$ Mn-O-Mn bonds forming the legs and the rungs of a ladder. The temperature dependence of the magnetic susceptibility exhibits well-defined maxima for all directions proving the low-dimensional magnetic character in BaMn$_2$O$_3$. The susceptibility and powder neutron diffraction data, however, show that BaMn$_2$O$_3$ exh…
We investigate the single hole dynamics in the triangular t-J model. We study the structure of the hole spectral function, assuming the existence of a 120 magnetic Neel order. Within the self-consistent Born approximation (SCBA) there is a strong momentum and t sign dependence of the spectra, related to the underlying magnetic structure and the particle-hole asymmetry of the model. For positive t, and in the strong coupling regime, we find that the low energy quasiparticle excitations vanish outside the neighbourhood of the magnetic Goldstone modes; while for negative t the quasiparticle excit…
We map certain highly correlated electron systems on lattices with geometrical frustration in the motion of added particles or holes to the spatial defect-defect correlations of dimer models in different geometries. These models are studied analytically and numerically. We consider different coverings for four different lattices: square, honeycomb, triangular, and diamond. In the case of hard-core dimer covering, we verify the existed results for the square and triangular lattice and obtain new ones for the honeycomb and the diamond lattices while in the case of loop covering we obtain new num…
Beyond a conventional classification of ferroelectricity, there is a class of materials where electronic degrees of freedom and electronic interactions are directly responsible for electric polarization and ferroelectric transition. This is termed electronic ferroelectricity. In this article, we review electronic ferroelectricity from a view point of frustration. Experimental and theoretical examinations in spin driven ferroelectric materials, recently termed multiferroics, are introduced. Spin frustration caused by competing magnetic interactions is of prime importance for this type of ferroe…
Emergence of partially disordered antiferromagnetism and isothermal magnetization plateau due to geometrical frustration in a metallic compound, Er2RhSi3
We present an element selective resonant magnetic x-ray scattering study of NdFe3(BO3)4 as a function of temperature and applied magnetic field. Our measurements show that the magnetic order of the Nd sublattice is induced by the Fe spin order. When a magnetic field is applied parallel to the hexagonal basal plane, the helicoidal spin order is suppressed and a collinear ordering, where the moments are forced to align in a direction perpendicular to the applied magnetic field, is stabilized. This result excludes a non-collinear spin order as the origin of the magnetically induced electric polar…
Spontaneous charge ordering occurring in correlated systems may be considered as a possible route to generate effective lattice structures with unconventional couplings. For this purpose we investigate the phase diagram of doped extended Hubbard models on two lattices: (i) the honeycomb lattice with on-site $U$ and nearest-neighbor $V$ Coulomb interactions at $3/4$ filling ($n=3/2$) and (ii) the triangular lattice with on-site $U$, nearest-neighbor $V$, and next-nearest-neighbor $V'$ Coulomb interactions at $3/8$ filling ($n=3/4$). We consider various approaches including mean-field approximat…
Using detailed synchrotron diffraction, magnetization, thermodynamic and transport measurements, we investigate the relationship between the mixed valence of Ir, lattice strain and the resultant structural and magnetic ground states in the geometrically frustrated triple perovskite iridate Ba$_{3}$NaIr$_{2}$O$_{9}$. We observe a complex interplay between lattice strain and structural phase co-existence, which is in sharp contrast to what is typically observed in this family of compounds. The low temperature magnetic ground state is characterized by the absence of long range order, and points t…
Recently, Co-based honeycomb magnets have been proposed as promising candidate materials to host the Kitaev spin liquid state. One of the front-runners is BaCo$_2$(AsO$_4$)$_2$ (BCAO), where it was suggested that the exchange processes between Co$^{2+}$ ions via the surrounding edge-sharing oxygen octahedra could give rise to bond-dependent Kitaev interactions. In this work, we present and analyze comprehensive inelastic neutron scattering studies of BCAO with fields in the honeycomb plane. Combining the constraints from the magnon excitations in the high-field polarized state and the inelasti…
A layered iron oxide \rfeo ($R$: rare-earth elements) is an exotic dielectric material with charge-order (CO) driven electric polarization and magnetoelectric effect caused by spin-charge coupling. In this paper, a theory of electronic structure and dielectric property in \rfeo is presented. Charge frustration in paired-triangular lattices allows a charge imbalance without inversion symmetry. Spin frustration induces reinforcement of this polar CO by a magnetic ordering. We also analyze an orbital model for the Fe ion which does not show a conventional long-range order.
Effects of geometrical frustration in low-dimensional charge ordering systems are theoretically studied, mainly focusing on dynamical properties. We treat extended Hubbard models at quarter-filling, where the frustration arises from competing charge ordered patterns favored by different intersite Coulomb interactions, which are effective models for various charge transfer-type molecular conductors and transition metal oxides. Two different lattice structures are considered: (a) one-dimensional chain with intersite Coulomb interaction of nearest neighbor V_1 and that of next-nearest neighbor V_…
Electronic and magnetic properties of molybdenum pyrochlores A2Mo2O7 are studied by the fully relativistic density-functional theory plus on-site repulsion (U) method, with focusing on the spin-glass insulating material Y2Mo2O7. We find that the system exhibits peculiar competition in energy between different magnetic states in the large-U insulating region. The magnetic competition cannot be explained by the conventional picture based on the geometrical frustration of isotropic Heisenberg antiferromagnetic exchange interactions. Through an analysis by using a generalized spin model, we find t…
The Hubbard model on the Kagomé lattice is investigated in a metallic phase at half-filling. By introducing anisotropic electron hopping on the lattice, we control geometrical frustration and clarify how the lattice geometry affects physical properties. By means of the fluctuation exchange (FLEX) approximation, we calculate the spin and charge susceptibilities, the one-particle spectral function, the quasi-particle renormalization factor, and the Fermi velocity. It is found that geometrical frustration of the Kagomé lattice suppresses the instability to various ordered states through the stron…
A current of electrons traversing a landscape of localized spins possessing non-coplanar magnetic order gains a geometrical (Berry) phase which can lead to a Hall voltage independent of the spin-orbit coupling within the material--a geometrical Hall effect. We show that the highly-correlated metal UCu5 possesses an unusually large controllable geometrical Hall effect at T<1.2K due to its frustration-induced magnetic order. The magnitude of the Hall response exceeds 20% of the ν=1 quantum Hall effect per atomic layer, which translates into an effective magnetic field of several hundred Tesla ac…
Magnetic frustration, which is well-defined in insulating systems with localized magnetic moments, yields exotic ground states like spin ices, spin glasses, or spin liquids. In metals magnetic frustration is less well defined because of the incipient delocalization of magnetic moments by the interaction with conduction electrons, viz., the Kondo effect. Hence, the Kondo effect and magnetic frustration are antithetic phenomena. Here we present experimental data of electrical resistivity, magnetization, specific heat and neutron diffraction on CePdAl, which is one of the rare examples of a geome…
We examine the optical conductivity σ(ω) and the chemical potential μ, together with the spin correlation, in the strong-coupling limit of a hole-doped two-dimensional triangular Hubbard model near half filling by using an exact diagonalization technique. In contrast to the case of a square lattice without frustration, the doping dependences of μand the Drude weight indicate that the charge degree of freedom is weakly coupled to the spin degree of freedom. However, we find that σ(ω) shows strong incoherent excitations extended to a higher energy region. This implies that geometrical frustratio…
We discuss a model scenario for multiferroic systems of type II (collinear spins) where the electric dipolar order competes with a frustrated magnetic order in determining the elastic distortions of the lattice ion positions. High magnetic frustration due to second neighbors exchange and small spin easy-axis anisotropy lead to the appearance of the so called quantum magnetic plateau states. Increasing the magnetic field above the plateau border produces composite excitations, where fractionalized spin tertions arise together with spontaneous dipolar flips (in the form of domain walls) and enha…
We investigate the Hubbard model on the anisotropic triangular lattice by means of the cellular dynamical mean field theory. The phase diagram determined in the Hubbard interaction versus temperature plane shows novel reentrant behavior in the Mott transition due to the competition between Fermi-liquid formation and magnetic correlations under geometrical frustration. We demonstrate that the reentrant behavior is characteristic of the Mott transition with intermediate geometrical frustration and indeed consistent with recent experimental results of organic materials.
We have observed geometrical frustration of quadrupolar and magnetic moments in dysprosium tetraboride, DyB4, where the rare-earth sites form a Shastry-Sutherland lattice. Resonant x-ray scattering at the LIII absorption edge of Dy was utilized. Analysis of the energy, polarization, temperature, and azimuthal-angle dependences of the E1 resonance of the (1 0 0) forbidden reflection show that the magnetic and quadrupolar components within the frustrated c plane have a short-range correlation, suggesting that the moments are fluctuating. By contrast, the basic antiferromagnetic component along t…
We study the ground state properties of the geometrically frustrated Hubbard model on the anisotropic checkerboard lattice with nearest-neighbor hopping $t$ and next nearest-neighbor hopping $t'$. By using the path-integral renormalization group method, we study the phase diagram in the parameter space of the Hubbard interaction $U$ and the frustration-control parameter $t'/t$. Close examinations of the effective hopping, the double occupancy, the momentum distribution and the spin/charge correlation functions allow us to determine the phase diagram at zero temperature, where the plaquette-sin…
Topological frustration (or topological mechanics) is the existence of classical zero modes that are robust to many but not all distortions of the Hamiltonian. It arises naturally from locality in systems whose interactions form a set of constraints such as in geometrically frustrated magnets and balls and springs metamaterials. For a magnet whose classical limit exhibits topological frustration, an important question is what happens to this topology when the degrees of freedom are quantized and whether such frustration could lead to exotic quantum phases of matter like a spin liquid. We answe…
The effect of geometrical frustration in a two-dimensional 1/4-filled strongly correlated electron system is studied theoretically, motivated by layered organic molecular crystals. An extended Hubbard model on the square lattice is considered, with competing nearest neighbor Coulomb interaction, V, and that of next-nearest neighbor along one of the diagonals, V', which favor different charge ordered states. Based on exact diagonalization calculations, we find a metallic phase stabilized over a broad window at V' ~ V even for large Coulomb repulsion strengths as a result of frustrating the char…
The dimerized quantum magnet BaCuSi$_2$O$_6$ was proposed as an example of "dimensional reduction" arising near the magnetic-field-induced quantum critical point (QCP) due to perfect geometrical frustration of its inter-bilayer interactions. We demonstrate by high-resolution neutron spectroscopy experiments that the effective intra-bilayer interactions are ferromagnetic, thereby excluding frustration. We explain the apparent dimensional reduction by establishing the presence of three magnetically inequivalent bilayers, with ratios 3:2:1, whose differing interaction parameters create an extra f…
We explore the magnetic phases in a Kondo lattice model on the geometrically frustrated Shastry-Sutherland lattice at metallic electron densities, searching for noncollinear and noncoplanar spin textures. Motivated by experimental observations in many rare-earth-based frustrated metallic magnets, we treat the local moments as classical spins and set the coupling between the itinerant electrons and local moments as the largest energy scale in the problem. Our results show that a noncollinear flux state is stabilized over an extended range of Hamiltonian parameters. These spin states can be quen…
To verify the effect of geometrical frustration, we artificially distort the triangular lattice of quasi-two-dimensional organic conductor $κ$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$ [BEDT-TTF: bis(ethylenedithio)terathiofulvalene] by analogous-molecular substitution and apply $^{13}$C NMR of bulk and substituted sites, electric conductivity, and static magnetic susceptibility measurements. The results indicate that the magnetic characteristics of the substituted sample are quantitatively similar to those of the pure sample. Moreover the magnetic characteristics at the substituted sites are also the same…
Geometrically Frustrated Quadrupoles on the Pyrochlore Lattice and Generalized Spin Liquids
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Laboratoire Léon Brillouin, CEA, CNRS, Université Paris-Saclay（里昂·布里渊实验室，法国原子能和替代能源委员会，法国国家科学研究中心，巴黎萨克雷大学）；Université Grenoble Alpes, CNRS, Institut Néel（格勒诺布尔阿尔卑斯大学，法国国家科学研究中心，尼尔研究所）
